Is it forbidden to extract additional copies of food coupons without the distributors' knowledge and obtain extra meals with them? If so, how can one atone for this action?

This act is forbidden, because it is consuming wealth unjustly, and it is deception and fraud. Allah Almighty said: (O you who have believed, do not consume one another's wealth unjustly). The Messenger of Allah, peace and blessings be upon him, said: (Indeed, your blood, your wealth, and your honor are sacred to you, like the sanctity of this day of yours, in this month of yours, in this land of yours, until the Day you meet Him… Verily, do not oppress, verily, do not oppress, verily, do not oppress; for the wealth of a person is not lawful except with his willing consent). He also said: (Whoever seizes the wealth of a Muslim without right will meet Allah Almighty while He is angry with him). And he also said: (Whoever deceives us is not of us, and scheming and deception lead to the Hellfire).

It is obligatory for whoever took food meals without right to repent to Allah, and to seek forgiveness from the rightful owner, or to pay him the price of these meals. If that is not possible, then he should give in charity on his behalf the value of the meals.